Why does a market maker skew quotes when inventory builds up?

You have been quoting $99.98$ bid, $100.02$ offered. A wave of sellers hits your bid and now you are long $50{,}000$ shares, far more than you want. You respond by moving your quote to $99.95$ bid, $99.99$ offered, still four cents wide, but shifted down.

Which cost component drives this, and why skew rather than just widen?